Pricing the financial Heston–Hull–White model with arbitrary correlation factors via an adaptive FDM

Abstract

This paper is concerned with the pricing procedure of one of the most challenging models known as the Heston–Hull–White partial differential equation (PDE) in option pricing, at which the model is a time-dependent 3D linear PDE including three mixed derivative terms. The model comes from the fact that the price, the volatility and the interest rate are assumed to be stochastic processes. To contribute and avoid huge discretized systems, an adaptive distribution of the nodes (viz, nonuniform nodes) is taken into account with emphasis on the hot area of the solution curve. New adaptive finite difference (FD) formulas of higher orders are constructed on these meshes. Then, a set of semi-discretized equations is attained which is tackled by a time-stepping method. Several financial tests are discussed in detail to reveal the superiority of the proposed approach.